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Question

# Four particles, each of mass m, are placed at the corners of a square of side a as shown in the figure. The position vector of the centre of mass is

A

a(^i+^j)

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B

a2(^i+^j)

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C

a(^i^j)

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D

a2(^i^j)

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Solution

## The correct option is B a2(^i+^j) The (x, y) co-ordinates of the masses at O, A, B and C respectively are (x1=0,y1=0),(x2=a,y2=0),(x3=a,y3=a) and (x4=0,y4=a). The (x,y) co-ordinates of the centre of mass are given by xCM=m×0+m×a+m×a+m×0m+m+m+m=a2 yCM=m×0+m×0+m×a+m×am+m+m+m=a2 Hence, the position vector of the centre of mass is a2(^i+^j), which is choice (b).

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